1 Bet Threat @ Casino Pauma
I saw a new Hold’Em type game at Casino Pauma last week, and I thought I’d work out the numbers and give it a try. The game is pretty simple. You bet an Ante before the hand begins. After seeing your two hole cards, you may bet 2x preflop, or check. After the flop, you may 1x bet or check. The turn, river, and the dealer’s hole cards are then revealed. The dealer qualifies with a pair of 6’s or better. If the dealer doesn’t qualify, all post-Ante wagers push. If the dealer beats your hand, you lose all your remaining bets. If you beat a qualified dealer hand, you win all your bets. If you beat a non-qualified dealer, you only win 1/2 your Ante.
The game is a bit calmer than Ultimate Texas Hold’Em, since you only have a single Ante, and you can check it down to showdown (in fact, this happens 69.8% of the time). Plus, players may like the fact that they can make the 2x and 1x bets only when they have an advantage. (I.e., all properly made 2x and 1x bets are +EV.) And the Ante is only a -11.4% loser, on average. The optimal player makes a 2x preflop bet 11.2% of the time, and a 1x flop bet on 25.5% of the time. The dealer qualifies 69.1% of the time. The game has relatively low variance, and I found myself increasing the Ante from the $5 minimum, to $10, and $15. (I’d never do that with UTH.)
The total outcomes for the optimal player strategy are listed in the table below, and show a house edge of 3.2% of the Ante.
| Outcome | Combinations | Frequency | Net | Return |
|---|---|---|---|---|
| Bet 2x and 1x and beat qualified dealer | 884,580,718,240 | 0.031804 | 4 | 0.127215 |
| Bet 2x and 1x and beat non-qualified dealer | 505,981,246,728 | 0.018192 | 0.5 | 0.009096 |
| Bet 2x and 1x and lose to qualified dealer | 374,729,986,984 | 0.013473 | -4 | -0.053891 |
| Bet 2x and 1x and lose to non-qualified dealer | 5,856,935,220 | 0.000211 | -1 | -0.000211 |
| Bet 2x and 1x and tie dealer | 25,182,150,868 | 0.000905 | 0 | 0.000000 |
| Bet 2x only and beat qualified dealer | 293,907,701,760 | 0.010567 | 3 | 0.031701 |
| Bet 2x only and beat non-qualified dealer | 387,449,913,432 | 0.013930 | 0.5 | 0.006965 |
| Bet 2x only and lose to qualified dealer | 524,307,039,216 | 0.018851 | -3 | -0.056552 |
| Bet 2x only and lose to non-qualified dealer | 76,858,269,780 | 0.002763 | -1 | -0.002763 |
| Bet 2x only and tie dealer | 25,553,189,772 | 0.000919 | 0 | 0.000000 |
| Bet 1x only and beat qualified dealer | 2,434,367,467,360 | 0.087524 | 2 | 0.175047 |
| Bet 1x only and beat non-qualified dealer | 1,467,870,962,280 | 0.052775 | 0.5 | 0.026387 |
| Bet 1x only and lose to qualified dealer | 1,215,166,965,412 | 0.043689 | -2 | -0.087379 |
| Bet 1x only and lose to non-qualified dealer | 17,931,292,692 | 0.000645 | -1 | -0.000645 |
| Bet 1x only and tie dealer | 164,852,060,176 | 0.005927 | 0 | 0.000000 |
| Bet ante only and beat qualified dealer | 3,363,692,256,360 | 0.120936 | 1 | 0.120936 |
| Bet ante only and beat non-qualified dealer | 4,003,403,426,760 | 0.143936 | 0.5 | 0.071968 |
| Bet ante only and lose to qualified dealer | 9,229,633,097,868 | 0.331836 | -1 | -0.331836 |
| Bet ante only and lose to non-qualified dealer | 1,896,770,105,748 | 0.068195 | -1 | -0.068195 |
| Bet ante only and tie dealer | 915,715,237,344 | 0.032923 | 0 | 0.000000 |
| Total | 27,813,810,024,000 | 1.000000 | -0.032157 |
I worked out the basic strategy for the game, just in case anyone wants to play the game. The strategy is actually pretty simple. Since the dealer qualifies with a pair of 6’s or better, you generally only bet the flop if there’s a qualified hand to beat. You can bet kickers and draws against a qualified flop, otherwise you should only bet a qualifying pair when there’s a board card lower than your pair, but 6 or higher.
The basic strategy below has an error rate of 4.5%, that only results in a cost of 0.23% to the player. So the practical house edge is 3.5% for the game.
| Wager | Player Hand | Rules |
|---|---|---|
| 2x | Pairs | 2x bet a pocket pair of 7’s or better, else check pocket 2’s thru 6’s. |
| Suited | Bet QJs, KTs, KJs, KQs, and A8s or better, else check all others. |
|
| Offsuit | Bet KQo, and ATo or better, else check all others. |
|
| 1x | Straight or better | Always bet. |
| Three-of-a-Kind | Always bet, except if trips on flop and less than 2nd nut kicker. | |
| Two Pairs | Bet if flop not paired, else bet if flop qualified (pair 6’s or better), else bet if board has undercard to pairs, else bet 9’s up or better, else check all others. |
|
| One Pair (qualified board has pair 6’s or better) |
Bet nut kicker, else bet flush draw, else bet open-ended straight draw with both holecards > 8, else check all others. |
|
| One Pair (small pair on board) |
Always check. | |
| One Pair (unpaired board) |
Bet if board has any qualifying undercards to pair, else bet pair w/ flush draw, else bet pair 9’s or better, else check all others. |
|
| No Pair | Bet 1st or 2nd nut flush draw, else check all others. |
There’s not much opportunity for collusion in the game. Knowledge of the hole cards of all 6 players will modify some of the preflop 2x decisions, but the frequency and value of these counter-(basic)strategy decisions aren’t enough to overcome the 3.2% house edge. Trust me, I’d have worked it out if it was worthwhile.
There’s two bonus bets offered, where the Pocket Bonus pays when your hole cards make a pocket pair, and the Final Hand bonus on your final 7-card hand. The paytables offered at Casino Pauma aren’t very good.
| Outcome | Combinations | Frequency | Payout (to-1) | Return |
|---|---|---|---|---|
| Pocket A’s | 6 | 0.004525 | 50 | 0.226244 |
| Pocket J’s – K’s | 18 | 0.013575 | 20 | 0.271493 |
| Pocket 2’s – T’s | 54 | 0.040724 | 8 | 0.325792 |
| no pair | 1,248 | 0.941176 | -1 | -0.941176 |
| Total | 1,326 | 1.000000 | -0.117647 |
| Outcome | Combinations | Frequency | Payout (to-1) | Return |
|---|---|---|---|---|
| Royal Flush | 4,324 | 0.000032 | 250 | 0.008080 |
| Straight Flush | 37,260 | 0.000279 | 50 | 0.013925 |
| Four-of-a-Kind | 224,848 | 0.001681 | 15 | 0.025210 |
| Full House | 3,473,184 | 0.025961 | 5 | 0.129805 |
| Flush | 4,047,644 | 0.030255 | 4 | 0.121020 |
| Straight | 6,180,020 | 0.046194 | 3 | 0.138581 |
| Three-of-a-Kind | 6,461,620 | 0.048299 | 2 | 0.096597 |
| Jacks Up | 17,385,408 | 0.129951 | 1 | 0.129951 |
| others | 95,970,252 | 0.717349 | -1 | -0.717349 |
| Total | 133,784,560 | 1.000000 | -0.054179 |
Discount Gambling 
1 Bet threat went live this week in Vegas (field trial at Texas Station)
Here are the approved paytables in New Jersey:
Hand Paytable A Paytable B Paytable C
Royal flush 250 to 1 250 to 1 100 to 1
Straight flush 50 to 1 50 to 1 50 to 1
Four-of-a-kind 10 to 1 15 to 1 12 to 10
Full house 6 to 1 5 to 1 5 to 1
Flush 4 to 1 4 to 1 4 to 1
Straight 3 to 1 3 to 1 3 to 1
Three-of-a-kind 2 to 1 2 to 1 2 to 1
Two pair (jacks 1 to 1 1 to 1 1 to 1
or better)
I think the paytables are terrible and will help this game have a very short life.
JAC, the 3 pay tables you list above are exactly the same on our game so I am not sure why you are so critical. You need to know the facts before making comments that don’t hold water. The pay tables at Pauma were Pay Table #3 which are the higher house edge. Each casino has its options so don’t shoot the game designer. Just curious, have you ever designed a game and placed it in a casino?
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